Problem: Solve for $x$ and $y$ using elimination. ${5x+3y = 28}$ ${-2x-3y = -13}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x+3y = 28}\thinspace$ to find $y$ ${5}{(5)}{ + 3y = 28}$ $25+3y = 28$ $25{-25} + 3y = 28{-25}$ $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ You can also plug ${x = 5}$ into $\thinspace {-2x-3y = -13}\thinspace$ and get the same answer for $y$ : ${-2}{(5)}{ - 3y = -13}$ ${y = 1}$